Stochastic Three Points Method for Unconstrained Smooth Minimization

An inexact and nonmonotone proximal method for smooth unconstrained minimization

An implementable proximal point algorithm is established for the smooth nonconvex unconstrained minimization problem. At each iteration, the algorithm minimizes approximately a general quadratic by a truncated strategy with step length control. The main contributions are: (i) a framework for updating the proximal parameter; (ii) inexact criteria for approximately solving the subproblems; (iii) ...

A modified secant method for unconstrained minimization

A Multidimensional Bisection Method for Unconstrained Minimization Problem

An extension of a new multidimensional bisection method for minimizing function over simplex is proposed for solving nonlinear unconstrained minimization problem. The method does not require a differentiability of function, and is guaranteed to converge to the minimizer for the class of strictly unimodal functions. The computational results demonstrating an effectiveness of algorithm for minimi...

A Nonmonotone Second - Order Steplength Method for Unconstrained Minimization

In this paper, a nonmonotone method based on McCormick’s second-order Armijo’s step-size rule [7] for unconstrained optimization problems is proposed. Every limit point of the sequence generated by using this procedure is proved to be a stationary point with the second-order optimality conditions. Numerical tests on a set of standard test problems are presented and show that the new algorithm i...

A regularized limited-memory BFGS method for unconstrained minimization problems

The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since LBFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a single iterat...